Interferometric Height Measurement

ABSTRACT

The invention relates to an interferometric method for measuring a height of a first region on a first surface, the first surface having first areas having first optical properties and second areas having second optical properties, the method comprising the steps of generating of first and second coherent light beams, reflecting at least the first coherent light beam from the first region into a first return beam and reflecting the second coherent light beam from a second region into a second return beam, measuring at least a first reflectivity of the first region, determining a topography-dependent phase shift of the first and second return beams for the height measurement based on the first reflectivity.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.11/481,101, filed on Jul. 5, 2006, entitled “Method and System forInterferometric Height Measurement,” the contents of which are herebyincorporated by reference.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention relates to the field of interferometric measuringmethods, for applications such as profile measurements, roughnessmeasurements, plainness measurements, and measurements of the radius ofcurvature as well as to an arrangement for implementing this method.

2. Description of the Related Art

Interferometers are being increasingly used in a number of productionprocesses to characterize and measure surfaces. Optical measuringdevices of this kind are distinguished by a high degree of measuringaccuracy. For manufacturing, it is desirable to make measurementswithout contacting the measured part to avoid damage. It is alsodesirable that measurements be fully automated.

A measuring device of this kind is the Laser Spot ScanningInterferometer (LASSI) described in U.S. Pat. No. 4,298,283 assigned tothe assignee of the present invention, incorporated herein by reference.The underlying measuring principle is based on scanning the surface tobe tested with two laser light beams which are simultaneously focusedadjacent to each other onto the surface. During this process, theoptical phase difference between the two light waves, which arereflected from the surface, changes linearly as a function of the heightdifference between the two laser spots on the surface. The phasedifference is determined by phase shifting. For this purpose, anelectro-optical light modulator is used which periodically shifts thephase difference between the two light waves by a fixed amount. At thesame time, the intensity of the two interfering light beams is measuredby a photodiode.

U.S. Pat. No. 5,392,116 which is assigned to the assignee of the presentinvention and is incorporated herein by reference, shows aninterferometric phase measurement method, which permits simultaneoussignal evaluation.

The orthogonally polarized light beams with the phase difference areinitially split by a beam splitter into several partial beam pairs,which, by means of a lens, are focused as parallel beams into a phaseshifter, a polarizer, and an array of light sensors. Phase differencesof the light beams create intensity differences between the beamsreceived by the different light sensors. High measuring speed andaccuracy are thus provided. When combined with means for directing twospatially separated orthogonally polarized beams on a surface, themethod and apparatus can be used to determine height differences alongthe surface.

The present invention aims to provide an improved interferometric methodand apparatus for enabling an increased precision of the interferometricmeasurement.

SUMMARY OF THE INVENTION

The present invention provides an improved interferometric method, whicheliminates the material-dependent phase shift from the total phase shiftof the reflected return beams. This material-dependent phase shift,which is also referred to as phase change on reflection (Fresnel phaseshift), occurs when light is reflected from a dielectric or a metal andis dependent on the optical properties of the reflecting surface, inparticular the index of refraction and the index of absorption and theoptical properties of the ambient medium.

When the measurement beam is moved over different areas of thereflecting surface having different optical properties thematerial-dependent phase shift changes correspondingly and thusintroduces a measurement error. By measuring the actual materialdependent phase shift for the region onto which the measurement beam iscurrently directed this measurement error is eliminated.

The determination of the current material-dependent phase shift isperformed based on a reflectivity measurement of the region on thereflecting surface onto which the measurement beam is directed. When theoptical properties of the reference surface which reflects the referencebeam is known, this facilitates determination of the material-dependentphase shift.

In accordance with a preferred embodiment of the invention both themeasurement beam and the reference beam are reflected by the samesurface. In this instance both the reflectivity of the region of thesurface reflecting the measurement beam as well as the reflectivity ofthe surface region which reflects the reference beam need to be measuredfor the determination of the material-dependent phase shift.

In accordance with a further preferred embodiment of the invention thefringe visibility value, which is delivered by a phase analyzer, is usedto further improve the precision of the calculation of thematerial-dependent phase shift.

The present invention is particularly advantageous for measuring thetopography of a surface which has a random distribution of areas havingtwo different optical properties. An example for such a surface is AlTiCsubstrate (Al₂O₃—TiC) which consists of Al₂O₃ in which TiC particleshaving randomly varying sizes and forms are embedded. Such an AlTiCsubstrate is used for the production of storage disk read/write heads.The interferometric method of the invention can thus be advantageouslyemployed for measuring the topography of the read/write head surface inthe production of such heads and for quality monitoring.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following text, preferred embodiments of the invention will bedescribed in greater detail by making reference to the drawings inwhich:

FIG. 1 shows a block diagram of an interferometric system,

FIG. 2 is illustrative of the random distribution of areas havingdifferent optical properties on the measurement surface,

FIG. 3 is a group of curves relating reflectivities tomaterial-dependent phase shifts,

FIG. 4 is a curve relating the reflectivity of the measurement beam tothe material-dependent phase shift.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

FIG. 1 shows interferometric system 100 having a laser 102 forgenerating laser beam 104. Laser beam 104 passes through λ/2-plate 106and is polarized by linear polarizer 108. The polarized laser beam 104goes through beam splitter 110 and is divided into coherent light beams112 and 114 by Wollaston-prism 116. Orthogonally polarized light beams112 and 114 pass through lens 118, beam splitter 120, lens 122, andobjective lens 126 before they are reflected from surface 128 to bemeasured. Light beam 112 is reflected from region 134 into return beam130. Light beam 114 is reflected from region 136 on surface 128 intoreturn beam 132.

A portion 138 is divided from light beam 112 by beam splitter 120 anddirected through optics 142 onto photo diode 144. Photo diode 144outputs a signal A which is proportional to the intensity of the lightbeam 112. Likewise beam splitter 120 provides portion 140 of light beam114 which is directed through optics 142 to photo diode 146 whichoutputs a signal B which is proportional to the intensity of light beam114.

Further, portion 172 of return beam 130 is provided by beam splitter 120and directed through optics 150 to photo diode 152. Photo diode 152outputs signal C which is proportional to the intensity of return beam130. Likewise beam splitter 120 provides portion 148 of return beam 132which is directed through optics 150 to photo diode 154 which providessignal D which is proportional to the intensity of return beam 132.

Wollaston-prism 116 and beam splitter 110 provide interference beam 158which results from the interference of the return beams 130 and 132 tophase analyzer 156. Phase analyzer 156 outputs a signal which isproportional to the total phase shift Δφ_(T) of return beams 130 and132. Further, phase analyzer 156 provides signal V which is the fringevisibility.

The signals A, B, C, D, Δφ_(T) and V are inputted into signal processingcomponent 160. By means of the signals A, B, C, D and V, signalprocessing component 160 eliminates the material-dependent phase shiftΔφ_(m) to provide the topography-dependent phase shiftΔφ_(b)(Δφ_(h)=Δφ_(T)−Δφ_(m)). By means of Δφ_(h) the exact topography ofthe surface 128 can be determined.

FIG. 2 shows a portion 162 of surface 128 (cf. FIG. 1). In the exampleconsidered here surface 128 belongs to a substrate which consists of afirst material with embedded particles of a second material; theparticles are randomly distributed and have random forms and shapes. Forexample the first material is Al₂O₃ with embedded particles of TiC.Surface areas which are constituted by the first material are designatedas a₁ and surface areas which are constituted by the second material aredesignated as a₂ in FIG. 2.

Light beam 112 is directed on portion 162 which results in a circularillumination pattern 164. Illumination pattern 164 covers a mixture ofsurface areas a₁ and a₂.

Likewise light beam 114 impinges on portion 166 of surface 128 which isalso composed of surface areas a₁ and a₂. Light beam 114 createsillumination pattern 168 on portion 166.

The average reflectivities of the regions covered by illuminationpatterns 164 and 168, respectively, are used as a basis to determine thematerial-dependent phase shift Δφ_(m). This is illustrated in FIG. 3.

The diagram of FIG. 3 shows the relationship between the reflectivity R₁of the region on surface 128 which is covered by illumination pattern164, the reflectivity R₂ of the region on surface 128 which is coveredby illumination pattern 168 and the resulting material-dependent phaseshift Δφ_(m). The reflectivity R₁ is obtained by dividing signal C bysignal A; likewise the reflectivity R₂ is obtained by dividing signal Dby signal B (cf. FIG. 1, signal processing component 160). With the R₁and R₂ reflectivity values the material-dependent phase shift isdetermined and subtracted from the total phase shift Δφ_(T) which isprovided by phase analyzer 156 (cf. FIG. 1).

The diagram of FIG. 3 can be obtained by a series of calibrationmeasurements. Alternatively the diagram of FIG. 3 can be obtained bymeans of a mathematical model:

Δϕ_(h) = Δϕ_(T) − Δϕ_(m) Δϕ_(m) = arcsin (αβ)$\alpha = \frac{r_{1}r_{2}{\sin \left( {\phi_{2} - \phi_{1}} \right)}}{{\left( r_{1} \right)^{2} - \left( r_{2} \right)^{2}}}$$\beta = {\frac{1}{2V}\frac{\left( R_{1} \right)^{2} - \left( R_{2} \right)^{2}}{\left( R_{1} \right)^{2} + \left( R_{2} \right)^{2}}}$where

Δφ_(h): topography-dependent_phase_shiftΔφ_(T): total_phase_shiftΔφ_(m): material-dependent_phase_shiftr₁: reflection_coefficient_of_materials_(—)1r₂ reflection_coefficient_of_material_(—)2 φ₁:phase_shift_caused_by_reflection_from_first_materialφ₂: phase_shift_caused_by_reflection_from_second_materialR₁: reflectivity_of_first_regionR₂: reflectivity_second_regionV: fringe_visibility

It is to be noted that α is a constant for a given pair of materials.This is because the reflection coefficient r₁ of the first material, thereflection coefficient r₂ of the second material as well as thematerial-dependent phase shift φ₁ caused by reflection from the firstmaterial and the material-dependent phase shift φ₂ caused by reflectionfrom the second material are material constants. Thus α only needs to becalculated once for a given material pair which constitutes a surfaceand can be stored for future reference.

The value of β needs to be recalculated for each position of theillumination patterns 164 and 168 as the reflectivities R₁ and R₂ canrandomly vary between the values |r1|² and |r2|².

As is apparent from the above mathematical model Δφ_(h)=Δφ_(T), ifR₁=R₂. Hence, when R₁=R₂ the total phase shift does not require acorrection. This enables one embodiment, where a height value is onlyoutputted, when R₁=R₂ as in this instance no correction of the totalphase difference is needed.

Alternatively only light beam 112 serves as a measurement beam whereaslight beam 114 serves as a reference light beam. In this instance lightbeam 114 is reflected from a reference surface having known opticalproperties. In this case only the reflectivity R₁ needs to be measuredfor the calculation of β and Δφ_(m).

This situation is illustrated in the diagram of FIG. 4 where the diagramof FIG. 3 is reduced to a single curve 170 which relates the measuredreflectivity R₁ to the material-dependent phase shift Δφ_(m). When theillumination pattern 164 of light beam 112 covers a region which onlyconsists of Al2O3 the additional phase shift Δφ_(m) is about 0 whereaswhen illumination pattern 164 covers a region which only consists of TiCthe phase shift Δφ_(m) is about 0.106 π which corresponds to a virtualheight of about 16 nanometers for a measurement wavelength of 633nanometers. This way a measurement error of up to 16 nanometers can beeliminated in the example considered here.

1. A machine-readable medium having a plurality of instructionsprocessable by a machine embodied therein, wherein said plurality ofinstructions, when processed by said machine, causes said machine toperform a method, said method comprising: generating a first coherentlight beam and a second coherent light beam; reflecting at least saidfirst coherent light beam from a first region into a first return beamand reflecting said second coherent light beam from a second region intoa second return beam; measuring at least a first reflectivity of saidfirst region; determining a topography-dependent phase shift of saidfirst return beam and said second return beam based on said firstreflectivity, wherein said determining step further comprisesdetermining said topography-dependent phase shift with reference to acurve relating said first reflectivity to a material-dependent phaseshift; and measuring a height based on said topography-dependent phaseshift.
 2. The machine-readable medium of claim 1, wherein said step ofdetermining said topography-dependent phase shift further comprisesdetermining said topography-dependent phase shift based on an opticalproperty of an area covered by said first region.
 3. Themachine-readable medium of claim 1, wherein said determining stepfurther comprises employing a reflectivity of a second region on areference surface having known optical properties.
 4. Themachine-readable medium of claim 1, wherein said determining stepfurther comprises: measuring a second reflectivity of a second region ona first surface; and determining the topography-dependent phase shiftbased on said first reflectivity and said second reflectivity.
 5. Themachine-readable medium of claim 1, wherein said determining stepfurther comprises determining a fringe visibility for use in determiningsaid topography-dependent phase shift.
 6. The machine-readable medium ofclaim 1, wherein said determining step further comprises determining atopography dependent phase shift through mathematical relationships,comprising: Δϕ_(h) = Δϕ_(T) − Δϕ_(m); Δϕ_(m) = arcsin (αβ);${\alpha = \frac{r_{1}r_{2}{\sin \left( {\phi_{2} - \phi_{1}} \right)}}{{\left( r_{1} \right)^{2} - \left( r_{2} \right)^{2}}}};$${\beta = {\frac{1}{2V}\frac{\left( R_{1} \right)^{2} - \left( R_{2} \right)^{2}}{\left( R_{1} \right)^{2} + \left( R_{2} \right)^{2}}}};$wherein: Δφ_(h) is a topography-dependent_phase_shift; Δφ_(T) is atotal_phase_shift; Δφ_(m) is a material dependent_phase_shift; r₁ is areflection_coefficient_of_first_area; r₂ is areflection_coefficient_of_second_area; φ₁ is a phaseshift_caused_by_reflection_from_first_area; φ₂ is aphase_shift_caused_by_reflection_from_second_area; R₁ is areflectivity_of_first_region; R₂ is a reflectivity_of_second_region; andV is a fringe_visibility.
 7. The machine-readable medium of claim 1,wherein: the determining step further comprises instructions forcalculating a material-dependent phase shift based on a first opticalproperty, a second optical property, and a first reflectivity of a firstregion; and the determining step further comprises instructions fordetermining a topography-dependent phase shift by subtracting amaterial-dependent phase shift from a total phase shift of a firstreflected coherent light beam and a second reflected coherent lightbeam.